The ratio of two marginal likelihoods gives us the factor by which the
average fit of the model in the numerator is better or worse than the
model in the denominator.
This is called the Bayes factor [1]}.
We can again leverage Bayes' rule to gain more intuition for how marginal
likelihoods and Bayes factors guide Bayesian model selection by
writing it in terms of the posterior probability of a model, \(M_{1}\) ,
among \(N\)  candidate models:
\(p(M_{1} \,|\, D) = \frac{p(D \,|\, M_{1})p(M_{1})}{\sum \limits _{i=1}^{N}p(D \,|\, M_{i})p(M_{i})}.\) 
